My wife likes the idea of me working out and being a triathlete, but she gets very upset very early in the training season.

She told me to just train right after work, but then i end up missing dinner time/family time.
Consequently, I do a fair share of training in the evening, when it should be "our time" after the kids go to sleep.
This is upsetting to her because (speculation) she doesn't think this is normal behavior. She thinks I'm "training" with another woman.
So I do a good number of runs/rides/OW swims late in the evening with a bad mental state after arguing. And I haven't even started HIM training yet.
I've skipped workouts to be home with her, and the thing i've got to learn is to keep my frustration about it to myself. DON'T mope around the house.

Our local pool has family hours right after lap swim so they come down and meet me and we have a nice afternoon.

I try to go to every single event my kids have. I usually miss more kid stuff due to working than training.
I try to be the one who suggests family time activities.

As mentioned, communication about goals, expectations, time commitments, etc. can help alleviate some friction.

Since you're already scheduling your training, sit down with your wife and go through the training plan to get her input as to how you can find 10 hrs (or what ever you plan is) per week, what times works the best for the entire family and then add family time to your training calendar. Take one day a week completely off, it'll do you good and allows for a full day with undivided family time. It's doable if all your time is accounted for, so forget any kind of other hobbies or social life for now. Long distance training is very tough on the family, but also tough on your friends (unless they're triathletes, then they'll love you for it!).

What it comes down to is a series of compromises and constant communication.

I'm extremely fortunate, my wife is a long distance triathlete, and we have no kids, so the time we have is completely ours to utilize how we see fit. We do plan our weeks together though, which allows us to find time for a social life as well (although, in all honesty, most of our friends are athletes as well)